Tuesday, June 09, 2015

W/m^2, Altitude and the Hour Record. Part III

In my previous posts on this topic I explored the impact of altitude on the hour record. You can recap by clicking on the links here:

W/m^2, Altitude and the Hour Record. Part I
W/m^2, Altitude and the Hour Record. Part II

In summary, the primary impacts on the speed attainable (or distance attainable for an hour) are:

1. Physiological - the reduction in sustainable aerobic power as altitude increases due to the reduced partial pressure of Oxygen, and

2. Physical - the reduction in aerodynamic drag as altitude increases due to the reduction air density.

Of course there are other factors - variable track surfaces and geometry, logistical, financial, physiological and so on, but for the purpose of this exercise I have confined analysis to the primary physiological and physical impacts.


These primary competing factors - reduced power and reduced drag combine to mean that in general an increase in altitude means a greater speed is attainable. In other words, the benefit of the lower air resistance at higher altitude typically outweighs the reduction in power. But not always.

The level of impact to speed is individual and is a function of each individual's physiological response to altitude - while the physics side of the equation is the same for everybody. I covered this in more detail in Part II of this series, and used data from several studies which provide four formula for the average impact of altitude on power output.

I plotted the different formula depending on whether athletes had acclimatised to altitude or not.



This chart should be fairly intuitive - further up in altitude you go, the more power you lose compared with sea level performance. The vertical scale of the chart amplifies the differences between them, which are not large, but also not insignificant either. A key element was the difference between athletes that had acclimated to altitude and those who had not.

Then I layered on that the physics impact of reducing air resistance, but the resulting chart was not quite as intuitive to follow and so I decided to revisit this another way.

Hence exhibit A below (click on the image to view larger version):



This should be reasonably straightforward to interpret, but even so I'll  provide some explanation.

The horizontal axis is altitude and the dark vertical lines represent the altitude of various tracks around the world.

The vertical axis is the proportion of sea level speed attainable.

The curved coloured lines represent the combined impact of both a reduction in power using each of the formula discussed in Part II of this series, combined with the reduction in air resistance.

So for example, if we look at the green line (Basset et al acclimated), this shows that as an cyclist increases altitude, they are capable of attaining a higher speed up until around 2,900 metres, and any further increase in altitude shows a decline in the speed attainable, as the power losses begin to outweigh the reduction in air density.

The track in Aigle Switerland represents around a 1% speed gain over London, while riding at Aguascalientes would provide for between a 2.5% to 4% gain in speed. Head to Mexico City and you might gain a little more, but as the chart shows, the curves begin to flatten out, and so the risk v reward balance tips more towards the riskier end of the spectrum.

Altitude therefore represents a case of good gains but diminishing returns as the air gets rarer. Once you head above 2,000 metres, the speed gains begin to taper off, and eventually they start to reduce, meaning there is a "sweet spot" altitude.

Caveats, and there are a few but the most important are:
-  any individual's sweet spot altitude will depend on their individual response to altitude - the plotted lines represent averages for the athletic groups studied;
- the formula used have a limited domain of validity, while the plotted lines extend beyond that, a point I also covered in Part II of this series;
- these are not the only performance factors to consider, but are two of the most important.

I suspect that the drop off in performance with altitude might occur a little more sharply for many than is suggested here. Nevertheless, the same principles apply even if your personal response to altitude is on the lower end of the range, and it is hard to imagine why anyone would suggest that heading to at least a moderate altitude track is a bad idea from a performance perspective.

Alex Dowsett rode 52.937km at Manchester earlier this year. At Aguascalientes he could reasonably expect to gain ~3.5% +/-0.5%  more speed, or just about precisely what Bradley Wiggins attained in London.

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Monday, June 08, 2015

Density matters

I saw a question today from someone who read recent comments about how high air pressure resulted in Brad Wiggins' hour distance being less than it might otherwise have been with more favourable conditions.

He was wondering if you can control air pressure in velodromes, or choose a time of year when it is lower. So can we do that?

Climate control


While there are velodromes where the inside air temperature is controllable (mostly northern hemisphere tracks located in cold climates), the control of air pressure is not something possible at any currently existing track that I'm aware of.

It would require quite a deal of engineering, in particular to provide an air lock / sealed environment that enables lots of people (and service vehicles) to enter /exit the building without affecting inside pressures and which meets emergency evacuation requirements for a large crowd, as well as fresh air to breathe. I don't see that happening any time soon.

Air locks do exist, e.g. at Aguascalientes velodrome in Mexico they use an air pressure differential to support the roof, but that means the air pressure inside the velodrome needs to be higher than outside. Not by much, but it will always need to be higher relative to local weather conditions, and inside the velodrome air pressure will still vary relative to outdoors.

So what about picking a better time of year?


Well let's look at the daily barometric pressure readings near London for the past three and a half years. Source for these charts is the National Physical Laboratory in the UK.

Barometric pressure London Jan-Dec 2012

Barometric pressure London Jan-Dec 2013

Barometric pressure London Jan-Dec 2014

Barometric pressure London Jan-June to date 2015

Looking at the above, it's pretty clear there is no obvious pattern to suggest a time of year when barometric pressure will be, on the balance of probabilities, lower.

Air density is what matters.

Air pressure of course is not the only variable. What really matters is attaining as low an air density as is physiological sensible. Air density along with a rider's aerodynamics, ie. their CdA, determines the energy demand for riding at a given speed, and lower air density is desirable for greater speed, provided of course the means to achieve that lower density doesn't reduce a rider's power to the extent performance ends up being worse. e.g. by riding at such high altitudes or temperatures that the rider's power output is compromised to a greater extent than the air density benefit provides.

Air density is a function of:
- air temperature
- barometric pressure
- altitude
- relative humidity

You can pretty much discount the latter as the changes in air density is very small with changes in humidity, although for the record humid air is slightly less dense than dry air (at same temperature, pressure and altitude).

Air density reduces with increasing temperature and altitude, and with reducing barometric pressure.

Since attempting to reduce air pressure either via climate control or by picking suitable times of year is not really an option, that leaves us with adjusting the other two variables - temperature and altitude.

I've discussed altitude before in this item. I'm going to revisit it in a future post in an attempt to simplify the impact of the variables involved.

Heating the air inside a velodrome is common, and this was attempted with some powerful portable heating devices during Jack Bobridge's unsuccessful attempt earlier this year, and in the case of attempts at most northern hemisphere tracks, the temperature has been dialled up to the rider's desired level.

Wiggins did specific heat acclimation work and reports are the temperature inside the velodrome was around 28-30C. That's pretty warm - going too hot can be detrimental as power losses can occur with inadequate cooling. As I said earlier, it's a balance between a physical benefit and a potential physiological cost.

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Wiggo's Hour

Just a short one today to update the chart from the one I posted here and on other social media forums. Click to see bigger version.


54.526km

Different reports of barometric pressure of 1031-1036hPa and air temp of 30.3C inside the track mean that Wiggins must have been exceptionally aerodynamic and recent work on his bike and position at the track suggest some good aero gains were made.

I estimate a power to CdA ratio of 2500-2550W/m^2 was required.

There are of course a range of assumptions:
Total mass: 82kg
Crr: 0.0023
Drivetrain efficiency: 98%
Altitude: 50m
Relative Humidity: 60%

If drivetrain efficiency is better, say 99% and Crr at 0.0020, then it drops the power to CdA ratio down to 2200-2220W/m^2.

and perfect pacing.

Just on that, my colleague Xavier Disley has once again produced a lap pacing chart - here it is:


That's a very slight fade over the course of an hour, which in my humble opinion is pretty much perfect. Opening few laps a bit hard, but that's understandable as a rider seeks to control the adrenaline rush with thousands in the crowd watching on and cheering.

The high air pressure did cost distance, and on another day perhaps 55km was within reach

As for going to high altitude, well there are many variables, but another 1-2km is feasible. See this item for more on that.

Well done to Brad Wiggins. That's sure a fine ride.

Read More......

Saturday, June 06, 2015

Pressure on the Hour

My colleague Xavier Disley did up a neat chart showing the impact the daily variability of barometric pressure can have on the distance attainable for an hour record, and how it's looking given the weather forecast when Xav last did the chart:


Nice - it shows how much breaking a record can still come down to a bit of luck with weather.

I think in Wiggins' case, assuming no major execution (i.e. totally crummy pacing) or mechanical issues, he'll break Dowsett's current mark no matter the weather as his power to drag ratio is sufficiently higher than Dowsett to overcome a slow air day.

But to set an outstanding mark such as Rominger's record, he'll need luck on his side. High pressure days are not good for speed.

Below is another version of this relationship between barometric pressure and distance attainable for four combinations of power and aerodynamic drag (CdA) values.


The chart is pretty self explanatory. For each combination of power and CdA chosen, the distance attainable reduces as barometric pressure increases.

That's because higher air pressure means a higher density of air molecules, and more air molecules to push out of the way requires more power.

A 60hPa difference in barometric pressure is equivalent to about 1km difference in distance attainable for the hour for the same power and CdA. That's a wide range of barometric pressure though, and variations are not normally quite that wide in most locations.

But a variation of half that is certainly possible over just a few days of varying weather as can be seen in Xavier's chart above.

I chose two power outputs: 430W and 450W, and two CdA values: 0.20m^2 and 0.19m^2. I don't know what Wiggins' power nor CdA value actually is or will be on the day, but for the sort of speeds he's likely to attain, these are in the ballpark.

It's the ratio of power (W) to aero drag coefficient CdA (m^2) that primarily determines the speed or distance attainable. hence why we refer to power/CdA ratio as measured by W/m^2. This chart covers a power to drag ratio range of 2150-2370 W/m^2.

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Friday, June 05, 2015

Where will Wiggo wind up?

Chart showing the progress of the UCI hour record since 1893 (click on it to view a bigger version):



The chart shows all the successful hour records recorded by the UCI. It doesn't show failed attempts.

The blue dots show the incremental increase in what is the absolute furthest distance attained.

The red dots show successful records for various categories of hour record but that did not surpass the furthest record for all categories up to that date.

For example, up until the early 1990s, the UCI had separate hour record categories for:
- amateur and professional riders
- above and below 600 metres altitude
- indoor and open air tracks

As a result, there were six categories of hour record for the period from about 1940 to the early 1990s.

And of course there have been bike/equipment regulation changes at times, most notably after Obree's and Boardman's records in the mid 1990s,

So where will Bradley Wiggins end up?


I'm pretty sure it'll be another red dot and not get close to Boardman's 1996 record and I doubt he'll beat Rominger's 1994 mark either. But he will likely beat Alex Dowsett's record (52.937km - the currently recognised record) by 1km or so.

I think anything above 54km will be very tough going. 54.5km perhaps if things go well. Closer towards 55km if everything is perfect.

Power 440-460W
CdA - who knows?

Say 0.200m^2.

Such a power range would net him around 53.5 - 54.4km at typical air density. 
On a low air density day that range would stretch to 54.5 - 55.4km. 

Weather forecast suggests low air density is unlikely although there is plenty of chat that they will raise the air temperature a lot, even up to 32C (yikes!).

So if velodrome air is heated to say 30C and air pressure is say 1020hPa, then at that power range and guessed CdA, the distance for a well paced effort will be in the 53.9 - 54.7km range.

Of course his CdA is the big unknown. Looks like he's been doing some work on it.

Drop that to 0.190m^2 and we can add about another lap (260 metres) to those estimated ranges.


Best of luck to Wiggo!

Read More......

Wednesday, February 25, 2015

Pursuit Spaghetti: Elite Pacing

The 2015 UCI track cycling world championships in Saint-Quentin-En-Yvelines, France, have recently concluded and there's been some on-line chatter about the pacing of Silver medallist and former world champion and world record holder Jack Bobridge during the final of the 4000 metre individual pursuit. Seen through the lens of his recent unsuccessful attempt at setting a world hour record, some are wondering "what was Jack was doing going out so fast?".

While he does start too hard and probably needs to reel that tendency in, I don't think it's quite the same as for his hour attempt. While many of the challenges are similar, pursuits are a different beast.

Some seemed to think he set out to catch his opponent in the final, and if you look at how he rapidly gained on his opponent in the early stages you'd think that might just be the case. Except I can't believe that would have been the strategy for various reasons (mainly since it would have required elite level kilo TT pacing to achieve it and so just wouldn't have happened). It also doesn't bear out in the data.

To explain this I thought I'd look at pursuit pacing at the elite level in general, as well as show what actually happened during the final between Bobridge and Gold medallist and winner Stefan Kueng of Switzerland.

Congratulations to Kueng by the way. He was Bronze medallist in 2013, Silver medallist in 2014 and is now the 2015 World Champion. That's a nice progression.

So here are some charts for you viewing pleasure.

The first shows the half lap (125 metre) times for each rider during their qualifying ride. it's a bit of a spaghetti junction, so I'll also show just the finalist's qualifying rides as well. Click the image to view a larger version.

2015 UCI World Championship 4000m individual pursuit qualifying
So what are we to make of this lot?

Well firstly I have highlighted the two lines for eventual winner Kueng (yellow) and Bobridge (red). This was their qualifying ride compared with everyone else (except for the Hong Kong rider whose times were a bit slow for this plot).

Also shown is a straight white line marking a slope representing a fade in pace of one second per kilometre. I use this as a guideline to assess whether a rider's pacing was good or poor. If you faded more quickly, then you started too hard, and the method of energy distribution wasn't optimal for attaining the least time possible.

It's pretty evident that many of those pacing lines are fading much more quickly than one second per kilometre. These are not novice riders but the best from their respective nations and some of the best in the world. This is a world championships and yet this most basic pacing mistake is still made.

That doesn't mean that pacing with more of a "flat line" is ideal either, although it's somewhat less of a sin than starting too hard and fading rapidly.

Pursuit pacing is a complex pacing optimisation problem. Dr Andy Coggan discusses this a little in the 3rd part of his excellent three part series: The Demands of the Individual Pursuit, so head there if you'd like to learn some more.

If you were able to speed up through the event, well it's also likely you've left some speed out there. Nailing this event takes practice and some years.

Let's clear away some of the noodles and look at the finalist's qualifying rides:

It's pretty clear that Bobridge starts hard and fades rapidly. Too hard and as a result, too rapidly. Kueng's pacing shows a negative split/getting faster in the second half, which suggests he left some pace out there.

Kueng had a qualifying advantage over Bobridge (and most of the field) in that Kueng rode in the final heat, while Bobridge rode the second heat. Kueng had earned his final heat advantage due to his Silver medal the previous year. This meant he knew his task to make the gold medal ride off was not to match Bobridge's time, which at that point was still the fastest qualifying time, but rather to beat his heat opponent and to beat the second best time up to that point, which was several seconds slower than Bobridge had ridden.

That meant Kueng's schedule could be more conservative than Bobridge's. This saves precious energy for the final, while Bobridge had to put all he had out there. As it turns out, Kueng's qualifying opponent (Alex Edmondson) faded in the final kilometre, which saw Kueng gaining but not quite catching him. That's pretty much the perfect scenario for a rider as you gain an increasing draft advantage in the final laps just when you need it, but don't waste precious energy passing your opponent. Bobridge caught and passed his opponent with 3 laps remaining, and it shows in his qualifying ride data.

The other two finalists show pretty reasonable pacing, however in the final laps their times blow out and rise rapidly. This is most likely because, like Bobridge, they caught their qualifying ride opponent and had to make a pass. As they approached the other rider they receive the benefit of some draft and that benefit increases the closer they approach, but then they have to make a pass and the acceleration to do that costs energy as well as track position. That's why you see that dip in track time followed by the rise. Once past their opponent, they are back out in the front with no more draft benefit and on fatiguing legs after having upped the power to make a pass - hence their lap times increase rapidly.

Here are the pacing plots for Kueng and Bobridge comparing their ride in qualifying (dashed lines) and in the gold medal final (solid lines):
Kueng and Bobridge pursuits: Qualifier and Final

We can see that Bobridge started his final almost exactly as he had done in the qualifying ride. Too fast again. This time his fade in pacing was even sharper. Kueng started a little harder than in his qualifier but still more conservatively than Bobridge. Kueng also started to fade at the halfway mark, just not as rapidly as Bobridge was dropping pace. It made for a fascinating race. Kueng only took the lead from Bobridge in the final half lap. Exciting stuff.

So thinking back to that first chart  - is this a common theme - that of elite riders starting too hard and riding a slower time than they might have done?

Well here are some more plots for the 2014 and 2013 world championships.

First the 2014 championships which were held in Cali, Colombia. This 250m wooden track, while covered, is exposed to the wind and so we can see the more variable pacing in the half laps times as riders battled slight head and tailwinds as they circulated the track. This undoubtedly makes pacing an even trickier challenge.

The two gold medal finalists are highlighted with the thicker yellow and red lines, yellow for the eventual winner. I'm guessing by looking at these lines that Kueng rides a bit more by feel than by pace and permitted his speed to vary more with the breeze. By and large most riders were fading by around 1 second per km or slightly more, so still some room for improvement.
2014 UCI World Championship 4000m individual pursuit qualifying

Here are the qualifying rides by the four finalists:

In 2013, the World Championships were held in Minsk, Belarus. Again the gold medal finalists are shown with yellow and red lines, but some of the pacing is just bizarre for world level.
2013 UCI World Championship 4000m individual pursuit qualifying

As with before, here are the qualifying rides for the four finalists:

So there you have it, three years of world championship pursuit spaghetti. Delicious.

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Tuesday, January 20, 2015

g force

No, not that kind of G-Force!

I mean the extra "weight" we feel pressing us down onto the bike or into the track when riding at speed around the curved banking of a velodrome.

If you really want to read up on g forces, then this Wikipedia page covers it.

First of all, "g force" isn't really a force, rather it's a measure of a rate of acceleration. It's one of those slightly confusing expressions.

g force is a way to "normalise" accelerations relative to that we experience every day due to gravity on the surface of the Earth. It's a way to gauge how much we'd "weigh" when experiencing an acceleration that's more or less than 1g.

When we are standing on the ground, we experience 1g (units are usually expressed a "g", not to be confused with grams). We are not actually accelerating, since the ground is there to stop us from falling, so instead we feel a force we call weight.

While we normally use standard international unit of metres per second squared (m/s^2) to express accelerations, it's common to express accelerations relative to that we experience on the surface of the Earth, which is defined a 1g.

If you have a mass of 80kg and are standing on the ground then you'll weigh 1g x 80kg. That's why many confuse weight with mass. They are not really the same thing, mass is an intrinsic property of an object, weight is the force it pushes down on the ground with. It's just that on when sitting on the surface of the Earth, an object with a mass of 80kg will also weigh 80kg.

However if you are accelerating upwards away from the Earth's surface (imagine you're travelling upwards in a rapidly accelerating elevator or rocket), then you'll experience more than 1g.

How much more depends on the rate of acceleration. If you happens to be accelerating upwards at 9.81 metres per second per second (which equals 1g), then you'd experience 2g, being acceleration due to gravity + the extra acceleration of the elevator or rocket. If you were able to stand on some bathroom scales while that acceleration is happening, then you'll "weigh" 80kg x 2g or feel like you now weigh 160kg. ugh.

Now keep in mind that an acceleration can be a change in speed and/or direction.

e.g. when a travelling in a car that turns around a corner, even through the road speed of the car may not change, we experience what feels like a force pressing us towards the opposite side of the car. Such lateral accelerations can also be expressed relative to 1g. Modern Formula 1 racing cars for example are capable of generating lateral corning accelerations of up to 6g.

g force on a velodrome


So whenever we are riding around the curved path on the turns of a velodrome, we are constantly accelerating towards the centre of the track, even though we may not be changing the bike's forward speed. As a result, we experience some lateral g forces when riding on velodrome, as well as the downward 1g due to gravity. What this means is the total g force we experience will be more than 1g. How much higher depends on our speed and the turn radius.

Calculating the rate of lateral acceleration when riding around a track is a pretty simple:
where:
- rider speed is in units of metres per second 
- 9.81 is the rate of acceleration due to gravity in metres per second squared
- rider turn radius is measured in metres

Estimating rider turn radius


To estimate a rider's turn radius, we start by estimating the track's turn radius.

First an overhead shot of a velodrome to get a sense of the general shape of a track (thanks to Google maps). This one happens to be a local outdoor track not far from where I live. It's a 333.33m concrete track. You can make out the faint blue band around the inside of the track, which is just inside of the track's black measurement line, the inner edge of which = 333.33 metres in length.
Now we can approximate the shape of the track as being two semi-circles joined by two straights. Here I superimposed some circles and lines to demonstrate:
Of course tracks are not exactly like this, in reality the shape of the turns are not perfectly circular, and the length of straights varies. They really do come in many different configurations. But as an approximation you can see from the diagram it's pretty good starting point. So to make a reasonable approximation of a track's turn radius at the black measurement line, all we need to know is the total length of the track, and the length of the straights.
Let's say you are riding a 250 metre track with 44 metre long straights. The turn radius around most of the turn will be approximately (250 - 2 x 44) / (2 x PI) = 25.8 metres.

Like I said, it won't be exactly that as in reality tracks have a variable turn radius but it's close enough for the purposes of this discussion. OK, that's great, we have the track's turn radius.

Now back to our lateral g force formula:
Now this formula asks for the rider's speed and turn radius, not the track's turn radius.

The rider's speed and turn radius is based on the position of their centre of mass (COM). Since a rider leans over when riding around the banked turn of a velodrome, then their COM speed and turn radius is less than the wheel's speed and the turn radius at the track where the tyre is rolling along.

Another diagram to help explain. You might need to look at a larger version - so click or right click on it to view a larger pic. ('The pic of a leaning rider I found on this blog item. Hope they don't mind me borrowing it - I can't however vouch for the physics discussed in that item).

When a rider at speed rides around the turn of a banked velodrome, they are leaning over. That means the turn radius of their COM is less than the turn radius of the track where the tyre is rolling along. So if you want to calculate the g force on a rider you really should be using the COM turn radius and speed, which is a bit of a pain because bikes use speed sensors that measure the wheel's speed.

To calculate COM radius and speed, you then need to know the rider's COM height and their lean angle (from the vertical). It's a little basic trigonometry. 

e.g. if a rider's COM is 1 metre (COM height will be about the same as floor to saddle height for a rider in an aggressive race position), and they are leaning over at 40 degrees from the vertical, then the rider turn radius = track turn radius - sin(40 degrees) x 1 metre. IOW we reduce the track turn radius by ~0.64 metres, which for our 250 metre track is about 2.5% of the track's turn radius. So not much, but enough that for some applications and analysis of track cycling data you need to take these things into account.

That then brings us to the question of how do we calculate the rider's lean angle? Well I'm going to leave that one for now because I'm getting further away from the issue of g forces than I'd really like. Suffice to say that we can reduce the estimated track turn radius and wheel speed by a couple of percent to estimate rider turn radius and rider COM speed.

Are you still with me?


OK, so we can reasonably estimate the lateral g force of a rider travelling around the turns of a track. But of course the rider also feels the force of gravity pulling them downwards. So the total g force acceleration into the track is the sum of those two acceleration vectors:
Which can be expressed as follows:

So there you have it.

How much g force does a rider feel in the turns?


If we use an estimated rider turn radius of ~25 metres for a typical 250 metre track with rider speeds ranging from 40km to 75km/h, here's what the estimated g forces are:
At elite hour record speeds of between 52-55 km/h, a rider will experience around 1.3g to 1.4g when riding the turns.

There is a physiological question to be considered, namely does this higher g force, which occurs twice per lap and lasts for about 2/3rds of the total time on track, cause any problems with blood circulation, is it sufficient to hamper performance?

I don't know, and I'm not sure if there's been anything more than speculation on this question. 1.3-1.4g doesn't sound like it'd cause too much of a problem to me, but who knows?

Track sprinters


Things get much more interesting for the world's best track sprinters, who experience around 2g in the turns during their flying 200 metre time trial. If you have a 95kg track sprinter flying around at 75km/h, the bike, wheels and tyres are supporting the equivalent down force of over 200kg.

This is why track sprint bikes and wheels have to be made extra strong, and also partly why track sprinters run extra high pressure in their specialist tubular tyres.

Would you put a 200kg rider on your bike?

Read More......

Monday, January 19, 2015

Some kilometres are longer than others

With the spate of attempts at the UCI world hour record over late-2014 and into 2015 due to the revised UCI rules making the record within reach of more riders, it has naturally sparked interest in discussing what matters for best performance in the event.

Jens Voigt started the latest round of hour record attempts at the UCI's Aigle track
I recently saw some chat on a triathlon forum speculating about who could do what distance and so on. All in good fun, but none of them actually go to a track to find out. If they did, they'd realise it's not quite as simple (or as hard) as they might make out.

It pretty much comes down to optimising four main elements:
  • maximising sustainable power output for an hour
  • minimising the physical resistance factors of riding on the track
  • technical execution / skill
  • logistics & resources
Some might add psychological factors to that list, but ultimately I consider these to be expressed within the outcomes of each of the above.

Regarding logistics, there are of course UCI requirements to be permitted an official attempt an hour record, e.g.: minimum time in anti-doping bio-passport program is mandatory at elite level or dope testing at age group level, application submitted in advance for approval to relevant levels of cycling administrations, all the technical requirements including international level commissaires to supervise, a UCI approved track, use of timing equipment, start gates, specified date and time of attempt, etc. You can't just rock up and ride whenever you like. Well you could but it would never be a sanctioned attempt.

Then of course you need to factor in enough solo rider time on track for preparation, and that costs money and time as well. Quality indoor tracks are not always local, and even if they are, getting solo time on the track is not always so easy, let alone cheap. For an elite professional rider whose job is to race on the road, it may be difficult to devote sufficient time to the task of preparing properly for a track event.

Of course assuming the paperwork is all in order and you can do your training, then sustainable aerobic power and aerodynamics are king and the rider's ratio of power to aerodynamic drag area is the single most important factor for how far they will go in the hour. But W/m^2 is not the only factor.

There are other physical resistance force factors, like the influence of air density which is a function of altitude, temperature and barometric pressure (and to a much lesser extent, humidity) and the rolling resistance of the track and tyres chosen. I discuss some of these in the following items:
Altitude and the Hour record Part I
Altitude and the Hour record Part II

Which leaves us with technical execution and skill factors, of which there are a couple of key items, namely:


Riding good lines


Riding a good line involves a couple of components, one is pretty obvious and involves not riding further than you need to around the bends. Ride wide and you ride further. Pretty simple given the track is all but two semi-circles joined together with two straight sections. OK, the actual shape of tracks are more subtlety curved but that's close enough to describe why riding wide adds distance to your travels around a lap.

Design of the Glasgow Velodrome

If you ride 10cm wider in the turns, you add 10cm x 2 x PI = 62.8cm per lap.

If the extra width is measured on the track's surface, well the actual addition to the distance the wheel travels is reduced by the cosine of the banking angle. e.g. say the track's turns are, on average, banked at 40 degrees, and you ride 10cm above the black line. Then the actual additional track radius ridden is cosine (40 degrees) x 10cm = 7.7cm, and the additional distance per lap = 7.7cm x 2 x PI = 48.1cm. Nearly half a metre.

Do that over 200 laps or so for an elite hour record and you'll ride ~100 metres more than you need to. And that's for riding only a hand's width above the black line.

London Velodrome used for the 2012 Olympics
Another more subtle ride line factor involves the shape and design of the banking and in particular the transitions from the straights to the turns and back again, and whether it's advantageous to ride a slightly wider line in the straights to aid the transitions. On the straights you don't suffer the same severe distance penalty of riding a wider "radius" as you do when riding wide in the turns, so you can explore marginal gains in this manner.

However there is no simple or single answer to this, it depends on the rider and the track geometry - all of which have subtle differences. This is a somewhat more complex optimisation problem and I'm not going to delve into it here.

So putting aside these subtleties, the shortest distance around the turns is to ride the track's black measurement line* - ride any further out from the black line and you ride more distance each lap than is necessary. For the hour record you only get credit for the official lap distance each lap, which is typically 250 metres per lap on most modern standard indoor velodromes although some tracks are shorter and some are longer.

* it is possible to ride inside the black line, however in such timed track events like the hour there are foam blocks placed around the inside line of the track to ensure the riders don't. Very skilled riders can however ride fractionally under the black line on some tracks but it is risky as hitting the foam blocks can disrupt your effort and wash off some speed. The shape of the track in that small space between the black line and the wide blue section varies from track to track and it can be good or not so good to ride in.


Foam blocks discourage riders from riding inside the black measurement line.

Now why are some kilometres longer than others?


Office distance for the hour record =
(Official lap distance)  x  (Number of full laps completed within the hour)
+ a pro-rata distance calculated for the final incomplete lap

I won't go into the formula used by the UCI to calculate the pro-rata distance of the final lap (that's actually deserving of a blog post on its own as the regulations are remarkably confusing).

It matters not how far you actually ride, you'll only be credited with the official minimum lap distance per lap. This is why track riders and coaches are focussed on lap times and not with bike speed, since lap times are the integral of all performance elements. Power meter and other data loggers are of course valuable in parsing out the individual elements of performance that go into attaining lap times, and helping to prioritise development opportunities.

How good are riders at riding the minimum distance necessary?


It varies. Quite a lot. Skilled track riders are typically much better, which is what you'd expect. But what sort of penalty would an unskilled rider face if they started out on a track effort?

Of course we can do lots of maths to figure out how much extra distance on average a rider might cover if they ride wide by so much, but in reality riders move up and down the track, sometimes riding a good line, other times not so good. Some riders are just better at it than others and some adapt to the track more quickly than others.

It'd be so much better if we could simply measure what people actually do rather than speculate.

Which had me thinking. I have some data like that already...

Not so long ago I was doing some performance testing involving half a dozen pro-continental road racers at an indoor 250m velodrome. One of the features of the data logging system used for the tests is an ability to calculate the distance ridden per lap using the wheel's speed sensor data combined with track timing tapes to know precisely when they pass a specific points on the track. With some clever maths this is enough to nail the actual distance ridden each lap to high precision.

In amongst the test data were some solo efforts of at least 10% of the distance of an elite hour record attempt (i.e. 20+ laps of consistent effort) and several such runs by each of the six riders. I figured the runs needed to be long enough to reasonably approximate what a rider might be expected to do over a longer distance/duration.

Of course absolute accuracy of the distance the wheels travel depends on having an accurate wheel circumference value and that value not changing a lot while riding. So I'm not going to assume that the absolute accuracy was perfect, even though the absolute error might typically be somewhat less than 1%. More than that would require an error in tyre circumference assumption of 20mm, which is a lot for those used to measuring such things. However in our favour is that even if such an error existed, it would be a consistent bias error.

So rather than concern myself with absolute accuracy, I thought I'd compare the measured average lap distance for each run with the shortest recorded legitimate lap. In this way if there is any bias error, it's impact on this analysis is minimised (i.e. both measurements would be out by the same proportional amount). By legitimate lap, I mean a full lap not ridden below the black line.

Here's a table summarising data collected from the six riders (in no particular order). Each rider has multiple runs although I haven't identified the riders in the table. What the first column shows is the average lap distance per run less the minimum legitimate lap distance for that same run. The distances are of course distance travelled by the wheel.


Now the riders possibly could ride a tighter line than they actually did for their shortest legitimate lap, meaning that these distances likely underestimate the extra distance ridden when compared with riding very tight to the black line.

For the moment though let's assume the shortest lap they rode during each run was the best they are capable of doing. Since they actually did it, I think that's a reasonable assumption.

The average extra distance ridden per lap varies from one rider to another. One rider consistently rode only 0.3-0.4 metres more per lap than their shortest distance lap, while another was consistently riding more than 2 metres extra per lap on average compared with their shortest legitimate lap. The rider with smallest extra distance per lap had a track racing background.

The second column shows what that average extra lap distance would mean if extrapolated to riding 200 laps of a 250m track (an official distance of 50.000km). For one rider they would be riding nearly half a kilometre further than their track skilled team mate. Yet if both completed exactly 200 laps in the hour, each would be credited with riding precisely 50km, even though one rider's wheels had travelled nearly 500m further than the other's.

In this case, 50.5km = 50.0km. Some kilometres are longer than others.

So what's that extra 500m cost in power terms?


Well for a rider with a CdA of ~0.23m^2, that extra 500 metres travelled requires they output ~11-12 watts more than if they were able to ride a a better line.

Or they'd need to find a 3% reduction in CdA to make up for their skill deficiency.

Remember these were well skilled, well trained and experienced pro-continential road racers and finding an extra 10W or losing another 3% of aero drag coefficient isn't such an easy thing to do.

So no matter your current skill level and experience, if you're expecting to ride such an event yet you have never trained to become proficient riding on the track, well you might want to chop half a kilometre or so from your estimated distance covered based on your power and aero data alone.

Better still, just get to a track a find out what you can actually do.

Likewise, when estimating power, or W/m^2 from the official hour record distances, you might need to add some watts for the technical proficiency of the rider. The less proficient, the more power is required to attain the same official distance.


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